Atkin-Lehner |
2+ 3- 5- 7+ 11+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
117810bk |
Isogeny class |
Conductor |
117810 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
2949120 |
Modular degree for the optimal curve |
Δ |
3677777012115360000 = 28 · 311 · 54 · 74 · 11 · 173 |
Discriminant |
Eigenvalues |
2+ 3- 5- 7+ 11+ -2 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-2521134,-1537389612] |
[a1,a2,a3,a4,a6] |
Generators |
[-933:1884:1] |
Generators of the group modulo torsion |
j |
2430995017485503655649/5044961607840000 |
j-invariant |
L |
4.5219621413378 |
L(r)(E,1)/r! |
Ω |
0.11982700707115 |
Real period |
R |
2.3585888067422 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999998659055 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
39270ck1 |
Quadratic twists by: -3 |